Computer monitors have inherent non-linear intensity relationships to voltage where the voltage an input voltage to the monitor to display a particular pixel. The non-linearity is referred to as a gamma (.gamma.) value, which when expressed as the power of a normalized voltage equals the normalized intensity. Gamma values typically range from about 1.5 to about 2.5. It has been common to correct for the non-linearity by looking up a gamma correction factor in a table for each pixel, and to adjust the voltage to be applied to the monitor in accordance with the gamma correction factor.
In addition, since the eye perceives intensity level ratios, rather than their absolute values, the intensity Levels should be incremented logarithmically, rather than linearly. Gamma correction thus takes into account the intensity ratios that the eye can perceive when controlling the voltage applied to the computer monitor.
A discussion of gamma correction in computer monitors may be found in the textbook "Fundamentals of Interactive Computer Graphics" by J. D. Foley and A. Van Damm, copyright 1982 by Addison-Wesley Publishing Company, pp. 594-597.
Most computer systems use an RGB color model, which represents color intensities in ranges of discrete voltages presented to red, green and blue electron gun control circuitry of e.g. a picture tube. In a YIQ color model, intensity is represented only by the Y component.
Normally, in drawn computer images gamma effects are not visible because the drawn images are typically pre-gamma corrected by the artist who selected gamma corrected colors when drawing. Digitized video is also usually pre-gamma corrected. However when images are to be resampled for resizing, or when video special effects are to be utilized such as fade-into another image, pixel arithmetic arises. The result of the pixel arithmetic can have visible deleterious effects in the displayed picture.
FIG. 1 is a graph of normalized pixel intensity for normalized voltage of a monitor. The curve 1 illustrates idealized linear intensity while the curve 2 illustrates gamma corrected intensity for a given voltage. Curve 3 illustrates the absolute gamma error, for which it may be seen that maximum gamma error occurs at a normalized voltage of about 0.5 V. There is no error at zero intensity and at full intensity.
While the graph of FIG. 1 appears to indicate that maximum error occurs at 50% of full scale voltage, this does not represent what effects occur when various intensities are added together.
FIG. 2 is a graph illustrating a percentage error of the intensity value represented by the absolute error. Exponential curve 4 results. It may be seen that the error approaches infinity as the voltage approaches zero (at zero there is a discontinuity where the error becomes zero). The percentage error only drops to relatively low levels when the normalized voltage reaches 0.9.
Thus it may be seen that low intensity signals are affected the most. While one would expect a marginal effect on most images because the focus of the picture tends to be toward the brighter parts, when adding two images, either both with low intensity or one with low intensity, the result is errors in both brightness and color, the latter since each color component may have a different gamma error. The result, particularly when images are added e.g. fading one image into another image, can be incorrect color and brightness.
In addition, drawn images tend to have saturated colors wherein they have intensities of either zero or 1 (maximum) while digitized images tend to have more intermediate values. Digitized images also tend to locality of brightness and color, i.e. a pixel will tend to have brightness and color close to that of the pixels surrounding it. This tends to hide the error because it will be smoothed away, but the images are incorrect. Nevertheless, experimental evidence shows that gamma error is most visible and pronounced on a RGB monitor, wherein a drawn image with high frequency components is mathematically processed.
It should be noted that if gamma correction is applied to the sum signal of two signals that are merged, this will not correct the more significant error of the low intensity signal. If the gamma correction of the sum signal were corrected in accordance with the gamma error of the low level signal, the high level signal will be corrected to an incorrect gamma correction factor.
To illustrate this, FIG. 3 is a graph of probability of error resulting from the combination of digitized video and a drawn image. The probability of a pixel or pixel component being at a particular intensity is illustrated as curves 6 and 7, which generally follow the form of curve 3 of FIG. 1. Curves 8 and 9 are intensity vs error curves. Thus it may be seen that greater error occurs at lower intensities of pixels or pixel components, and thus drawn images (curve 7) would tend to exhibit visible effects of this error, whereas video images (curve 6) would not. FIG. 3 is not drawn to vertical scale for any of the curves.